Adenine and adenosine salvage pathways in erythrocytes and the role of S-adenosylhomocysteine hydrolase

Transcription

1 Adenine and adenosine salvage pathways in erythrocytes and the role of S-adenosylhomocysteine hydrolase A theoretical study using elementary flux modes Stefan Schuster and Dimitar Kenanov Department of Bioinformatics, Friedrich Schiller University, Jena, Germany Keywords elementary flux modes; enzyme deficiencies; erythrocytes; nucleotide metabolism; salvage pathways Correspondence S. Schuster, Department of Bioinformatics, Friedrich Schiller University, Ernst-Abbe- Platz 2, Jena, Germany Fax: Tel: schuster@minet.uni-jena.de (Received 6 June 2005, revised 5 August 2005, accepted 19 August 2005) doi: /j x This article is devoted to the study of redundancy and yield of salvage pathways in human erythrocytes. These cells are not able to synthesize de novo. However, the salvage (recycling) of certain nucleosides or bases to give nucleotide triphosphates is operative. As the salvage pathways use enzymes consuming as well as enzymes producing, it is not easy to see whether a net synthesis of is possible. As for pathways using adenosine, a straightforward assumption is that these pathways start with adenosine kinase. However, a pathway bypassing this enzyme and using S-adenosylhomocysteine hydrolase instead was reported. So far, this route has not been analysed in detail. Using the concept of elementary flux modes, we investigate theoretically which salvage pathways exist in erythrocytes, which enzymes belong to each of these and what relative fluxes these enzymes carry. Here, we compute the net overall stoichiometry of build-up from the recycled substrates and show that the network has considerable redundancy. For example, four different pathways of adenine salvage and 12 different pathways of adenosine salvage are obtained. They give different glucose yields, the highest being 3 : 10 for adenine salvage and 2 : 3 for adenosine salvage provided that adenosine is not used as an energy source. Implications for enzyme deficiencies are discussed. The human erythrocyte has been a subject not only of intense experimental research but also of many modelling studies [1 6] because this cell is of high medical relevance, is readily accessible and its metabolism is relatively simple. Human red blood cells are not able to synthesize de novo. However, they involve salvage pathways, that is, routes by which nucleosides or bases can be recycled to give nucleotide triphosphates [7]. The exact structure of salvage pathways (for example, starting from adenine or adenosine) has not yet been analysed in much detail. Because the salvage pathways involve enzymes consuming, such as phosphoribosylpyrophosphate synthetase and adenosine kinase, as well as enzymes producing, such as pyruvate kinase, it is not straightforward to see whether a net production of can be realized. Besides adenine and adenosine, hypoxanthine is usually considered a major substrate of salvage pathways [7]. However, in mature erythrocytes, hypoxanthine cannot be recycled to give because of the lack of adenylosuccinate synthetase, which is necessary for transforming inosine 5 -monophosphate (IMP) into AMP [8]. Here, we analyse theoretically how many salvage pathways exist, which enzymes each of these involves and in what flux proportions (i.e. relative fluxes) the enzymes operate. Moreover, we compute the net overall stoichiometry of anabolism. (Throughout the paper, by anabolism or buildup, Abbreviations RT, adenine phosphoribosyltransferase; IMP, inosine 5 -monophosphate; SAHH, S-adenosylhomocysteine hydrolase; SAM, S-adenosylmethionine FEBS Journal 272 (2005) ª 2005 FEBS

2 S. Schuster and D. Kenanov A theoretical study using elementary flux modes we mean the production of from salvaged substrates rather than de novo synthesis.) As for pathways involving adenosine, a plausible assumption is that adenosine kinase would be used. However, Simmonds and coworkers [8 11] found that an elevation of can occur in the absence of adenosine kinase, as long as adenine phosphoribosyl transferase (R transferase, or RT) is present. This is indicative of an alternative salvage pathway in human erythrocytes, and evidence was presented [8 11] that S-adenosylhomocysteine hydrolase (SAHH, EC ), which is difficult to assess in vivo, is involved in these pathways. Since adenine is a substrate of RT, the elevation of in the absence of adenosine kinase shows that adenine must be released in the process before being incorporated into. Indeed, studies on purified SAHH showed that several purine nucleosides and analogues can release adenine resulting from interaction with this enzyme [12]. One of these analogues is S-adenosylmethionine (SAM) [11] which can be taken up through the erythrocyte membrane and is abundant in all living cells [9,11]. Simmonds and coworkers [8 11] investigated the pathway of buildup from SAM, though not by a detailed stoichiometric analysis. SAM is converted into S-adenosylhomocysteine (the substrate of SAHH) by enzymes from the class of methyltransferases (EC x). In the catalytic process of SAHH, additionally a spontaneous decomposition of the metabolite 3 -ketoadenosine occurs, leading to free adenine and 3 -ketoribose [13]. The adenine moiety can then be processed through RT. Although under normal circumstances this pathway is not expected to produce significant amounts of adenine, it is important to mention the possibility this pathway offers not only for generation (in erythrocytes or other types of cells harbouring SAHH) but also for the conversion of nucleoside analogues derivatives to nucleotides. This is very important from the medical point of view because these analogues are used in chemotherapy, where one is interested in preventing an undesired transformation of these analogues [10]. Also in our present theoretical study, we include the enzyme SAHH and a methyltransferase. Our analysis is based on the concept of elementary flux mode. This term refers to a minimal group of enzymes that can operate at steady state with all the irreversible reactions used in the right direction [14,15]. If only the enzymes belonging to one elementary mode are operative and, thereafter, one of the enzymes is inhibited, then the remaining enzymes can no longer be operational because the system cannot any longer maintain a steady state. Elementary mode analysis has been applied to various systems (e.g [3,16 19]). C akiýr et al. [6] applied this method to energy metabolism in erythrocytes. A concept related to that of elementary modes is that of extreme pathways [20]. A comparison of the two concepts was made by Klamt and Stelling in [21]. Many biochemically relevant products are synthesized or degraded on multiple routes. Elementary modes provide a powerful tool for determining the degree of multiplicity and, thus, of redundancy [18,19]. This is of particular interest for the study of diseases based on enzyme deficiencies [3,6]. There are several diseases caused by enzyme deficiencies in nucleotide metabolism. Examples are provided by the following diseases: severe combined immunodeficiency, 2,8-dihydroxyadenine urolithiasis, and Lesch Nyhan syndrome, caused by deficiencies in the adenosine deaminase (ADA), - RT, and hypoxanthine guanine phosphoribosyltransferase (HGPRT), respectively [22]. However, these diseases are related mainly to cells other than erythrocytes, such as lymphocytes. In the case of severe deficiencies, a possible modelling strategy is to consider the enzyme to be fully inhibited and examine which elementary modes are still present in the system. This allows us to detect bypasses, if any, or in other words to estimate the redundancy of the system. In this way one can predict which final products are still being produced and assess the impact of the deficiency on the patient s metabolism. This, in turn, helps us decide which enzyme deficiencies can be considered as not harmful for the cell. Here, we specifically perform this analysis for anabolism in erythrocytes. Results and Discussion As outlined in the Introduction, we compute elementary flux modes in nucleotide metabolism. The reaction scheme is shown in Fig. 1. The scheme is explained in more detail in the Experimental procedures. The goal is to analyse the redundancy and molar yields of salvage pathways. This analysis is carried out consecutively for different substrates. For the simulation of adenine and adenosine salvage, we do not include methyltransferase and SAHH. Adenine salvage In the first simulation, we consider, in addition to the external metabolites mentioned in Experimental procedures, adenine as external, to find out how can be synthesized starting from adenine. Running metatool on this network gives 153 elementary modes (supplementary Table S1). Four of them produce FEBS Journal 272 (2005) ª 2005 FEBS 5279

3 A theoretical study using elementary flux modes S. Schuster and D. Kenanov membrane GLCext GLCim GLC HK G6PDH G6P GL6P PGLase GO6P GL6PDH PGI F6P N GSSGR NH R5PI CO 2 R5P RU5P Xu5PE X5P PFK TKI FDP S7P GA3P ALD 2GSH GSHox GSSG TA GA3P TPI DHAP F6P E4P TKII NAD GAPDH NADH GA3P DPGM PGK 1,3 DPG NADH NAD 2,3DPG DPGase 3PG PGM 2PG EN PEP PK PYR LDH LAC PYRtrans LACtrans PYRext LACext N a + Na + leak N a + NaK K + + K + K leak ase SAHH2 HCY S-AdoHcy MetAcc MT Acc SAM 3'KetoRibose ADENINE AMP PRPP ApK SAHH1 RT PRPPsyn AMP IMP AMPDA NUC AK NUC R5P ADO AMP R1P PRPP HGPRT HXtrans HYPX ADA HCY PRM INO PNPase HYPXext SAMext Fig. 1. Model representing glycolysis, the pentose phosphate pathway and purine metabolism in red blood cells, including a methyltransferase and two possible ways of operation of S-adenosylhomocysteine hydrolase (SAHH1 and SAHH2) (extended from [10]). Transport reactions of adenine and adenosine across the cell membrane are not shown for simplicity s sake. For abbreviations of enzymes and metabolites, see Table 1. (modes , supplementary Table S1). They are listed in Table 2. Note that in Tables 2 5, the numbers in the brackets denote relative fluxes carried by the corresponding enzymes. + and indicate whether the elementary mode remains intact if the enzyme in the column heading is deficient. It can be seen that mode II.1 (here and in the following, mode x,y means mode y in Table x) uses glycolysis, the oxidative pentose phosphate pathway, and the enzymes d-ribose-5p-isomerase (R5PI), phosphoribosylpyrophosphate (PRPP) synthase, RT and adenylate kinase (ApK). Mode II.2 involves glycolysis, both the oxidative and nonoxidative parts of the pentose phosphate pathway, and the enzymes R5PI, PRPP synthase, RT and ApK, yet in proportions different from mode II.1. It is worth noting that glucose-6p-isomerase (PGI) is used backwards (in the direction of glucose-6-phosphate formation) and that fructosediphosphate aldolase and triosephosphate isomerase (TPI) are not involved. Mode II.3 involves ALD and TPI in addition but not PGI (Table 2). As for mode II.4, it is worth noting that it does not comprise the oxidative pentose phosphate pathway. Fructose-diphosphate aldolase, TPI as well as PGI are involved in that mode. Importantly, none of these pathways involves adenosine kinase (AK), nor do they run via adenosine. Part of the pentose phosphate pathway is needed to provide the R5P necessary for the ribose moiety in the nucleotides. As mentioned in the Introduction, due to the existence of both consuming reactions and producing reactions in the salvage pathways, it is not easy to see whether a net production of is possible. Note that only a certain fraction of the produced in the lower part of glycolysis is obtained in the net balance because the remaining fraction is needed to upgrade adenine. Let us analyse, for example, mode II.1. Two moles of adenine are converted into two AMP by RT. The supply of two PRPP for this conversion requires two in PRPP synthase FEBS Journal 272 (2005) ª 2005 FEBS

4 S. Schuster and D. Kenanov A theoretical study using elementary flux modes Table 1. List of all enzymes and metabolites included in the model. Abbreviation Full name EC number Enzyme ADA Adenosine deaminase RT Adenine phosphoribosyltransferase AK Adenosine kinase ALD1 Fructose-diphosphate aldolase AMPDA Adenosine monophosphate deaminase APK Adenylate kinase C5MT Cytosine-5-methyltransferase DPGase Diphosphoglycerate phosphatase DPGM 2,3-Diphosphoglycerate mutase EN Enolase G6PDH Glucose-6P dehydrogenase GAPDH Glyceraldehyde-3P dehydrogenase GL6PDH 6P-Gluconate dehydrogenase GSHox Glutathioneperoxidase GSSGR Glutathione reductase HGPRT Hypoxanthine guanine phosphoribosyltransferase HK Hexokinase LDH Lactate dehydrogenase NUC AMP phosphatase PFK1 Phosphofructokinase PGI Glucose-6P-isomerase PGK1 Phosphoglycerate kinase PGLase 6P-Gluconolactonase PGM Phosphoglycerate mutase PK Pyruvate kinase PNPase Purine nucleoside phosphorylase PRM Phosphoribomutase PRPP synthase Phosphoribosylpyrophosphate synthetase R5PI D-Ribose-5P-isomerase SAHH S-Adenosylhomocysteine hydrolase TA Transaldolase TK Transketolase TPI Triosephosphate isomerase XU5PE D-Xylulose-5P-3-epimerase Metabolites 1,3 DPG 1,3-Diphospho-D-glycerate 2,3 DPG 2,3-Diphospho-D-glycerate 2PG 2-Phospho-D-glycerate 3 -keto ribose 3 -Keto ribose 3PG 3-Phospho-D-glycerate Acc Acceptor for methyl group Adenine Adenine Ado Adenosine Adenosine 5 -diphosphate AMP Adenosine 5 -monophosphate Adenosine 5 -triphosphate CO2 Carbon dioxide DHAP Dihydroxyacetone phosphate E4P D-Erythrose 4-phosphate F6P Fructose 6-phosphate FDP Fructose 1,6-diphosphate G6P Glucose 6-phosphate Table 1. Continued. Abbreviation Full name EC number GA3P GL6P GLC GO6P GSH GSSG HCY HYPX IMP INO K + LAC MetAcc Na + NAD NADH N NH PEP PRPP PYR R5P RIP RU5P S-AdoHcy S7P SAM X5P Glyceraldehyde 3-phosphate D-Glucono-1,5-lactone 6-phosphate Glucose 6-Phospho-D-gluconate Reduced glutathione Oxidized glutathione L-Homocysteine Hypoxanthine Inosine 5 -monophosphate Inosine Potassium L-Lactate Methylated acceptor Sodium Nicotinamide adenine dinucleotide Nicotinamide adenine dinucleotide reduced Nicotinamide adenine dinucleotide phosphate Nicotinamide adenine dinucleotide phosphate reduced Phosphoenolpyruvate 5-Phospho-alpha-D-ribose 1-diphosphate Pyruvate D-Ribulose 5-phosphate D-Ribose 1-phosphate D-Ribulose 5-phosphate S-Adenosyl-L-homocysteine D-Sedoheptulose 7-phosphate S-Adenosyl-L-methionine D-Xylulose 5-phosphate R transferase and PRPP synthase together form four AMP. Using another four, these are transformed into eight in ApK. Due to the special flux distribution, seven are consumed in hexokinase and five in phosphofructokinase. In glycolysis, 20 mol are produced; 10 in each of phosphoglycerate kinase and pyruvate kinase. This gives an balance of )2 4) ¼ 2. Note that the lower part of glycolysis has to run five times as fast as R transferase to make this positive balance possible. The glucose yields (that is, the ratios of production over glucose consumption fluxes) of modes II.1-II.4 are 2 : 7, 1 : 6, 1 : 4 and 3 : 10, respectively. Note that these are the yields for the buildup of from adenine rather than from as usually indicated for glycolysis. Mode II.4 has the highest yield. It can be shown that the flux distribution realizing the highest yield always coincides with an elementary mode or a linear combination of two modes with the same maximum yield [14]. Thus, there FEBS Journal 272 (2005) ª 2005 FEBS 5281

5 A theoretical study using elementary flux modes S. Schuster and D. Kenanov Table 2. Elementary modes producing from adenine. Elementary modes ADA AK PNPase RT 1. (5 PGI) (5 ALD) (5 TPI) (10 GAPDH) (10 PGM) (10 EN) (10 LACex) ( 4 ApK) (2 PGLase) (4 GSSGR) (2 R5PI) (7 HK) (5 PFK) (10 PGK) (10 PK) (10 LDH) (2 RT) (4 GSHox) (2 PRPPsyn) (2 G6PD) (2 GL6PDH) 7 GLC + 2 Adenine ¼ 2CO LACext ()10 PGI) (5 GAPDH) (5 PGM) (5 EN) (5 LACex) () 2 ApK) (16 PGLase) (32 GSSGR) (6 R5PI) (10 Xu5PE) (5 TKI) (5 TKII) (5 TA) (6 HK) (5 PGK) (5 PK) (5 LDH) RT (32 GSHox) PRPPsyn (16 G6PD) (16 GL6PDH) 6 GLC + Adenine ¼ 16 CO LACext + 3. (2 ALD) (2 TPI) (5 GAPDH) (5 PGM) (5 EN) (5 LACex) () 2 ApK) (4 PGLase) (8 GSSGR) (2 R5PI) (2 Xu5PE) TKI TKII TA (4 HK) (2 PFK) (5 PGK) (5 PK) (5 LDH) RT (8 GSHox) PRPPsyn (4 G6PD) (4 GL6PDH) 4 GLC + Adenine ¼ 4CO LACext + 4. (10 PGI) (8 ALD) (8 TPI) (15 GAPDH) (15 PGM) (15 EN) (15 LACex) ( 6 ApK) (2 R5PI) ( 2 Xu5PE) -TKI -TKII -TA (10 HK) (8 PFK) (15 PGK) (15 PK) (15 LDH) (3 RT) (3 PRPPsyn) 10 GLC + 3 Adenine ¼ 15 LACext + 3 can be no flux distribution of adenine salvage enabling an glucose yield higher than 0.3. Interestingly, none of the producing modes involves the 2,3-diphosphoglycerate phosphatase (DPG) bypass. As this would circumvent the enzyme phosphoglycerate kinase, the yield of glycolysis would be decreased, to such an extent that no buildup from adenine would be possible. Most of the remaining elementary modes of the first simulation can be interpreted as degradation of to hypoxanthine. One elementary mode describes the 2,3DPG bypass of glycolysis, with a zero balance. As we consider as internal, normal glycolysis implying a transformation of into is not computed. Adenosine salvage In the second simulation, we analysed buildup from adenosine. Therefore, we consider adenosine (but not adenine) to be external. This gives rise to 97 elementary modes (Supplementary Table S2). Twelve modes (numbers 10, 15, 20, 54 59, 77, 85, and 92 in Table S2) produce from adenosine (Table 3). All of these involve AK and ApK. Mode III.1 is made up of glycolysis, AK and ApK and does not involve any pentose phosphate pathway enzyme. The flux ratio between the upper and lower parts of glycolysis is, as in pure glycolysis, 1 : 2. The flux ratio between AK as well as ApK and the upper part of glycolysis is 2 : 3. Thus, 2 out of six produced from in glycolysis are used to convert adenosine into AMP. The latter is upgraded by ApK to give. In total, 2 mol of are built up from adenosine per 3 mol of glucose. Modes III.2 and III.3 involve different combinations of glycolysis and the pentose phosphate pathway as well as AK and ApK. The involvement of the pentose phosphate pathway is not, however, essential for build up in these modes. It merely lowers the glucose yield. Modes III.4-III.9 do not start from glucose but solely from adenosine. This is used not only as the source for buildup but also as an energy source. Adenosine is degraded into hypoxanthine (which is excreted) and ribose-1-phosphate, which is transformed, by the pentose phosphate pathway, into glycolytic intermediates. Modes III.10-III.12 use both glucose and adenosine as energy sources, in different proportions. Modes III.4, III.7 and III.11 involve the 2,3DPG bypass. Again, there is no mode involving the 2,3DPG bypass when glucose is used as the only energy source (modes III.1-III.3) because the glucose yield would then be so low that no buildup would be possible. The adenosine yields of the -producing modes are 1 for modes III.1-III.3, 1 : 4, 2 : 5, 1 : 4, 1 : 4, 8 : 17, 5 : 14, 2 : 3, 1 : 4 and 5 : 8 for modes III.4-III.12, respectively. Thus, modes starting from glucose and adenosine transform the latter completely into, which implies that glucose is the only energy source. By contrast, in the modes starting solely from adenosine, part of this substrate is used as an energy source, so that the yield is lower. Inclusion of SAHH As mentioned in the Introduction, there is experimental evidence that S-adenosylmethionine can be used by erythrocytes for buildup [8 11]. To analyse this 5282 FEBS Journal 272 (2005) ª 2005 FEBS

6 S. Schuster and D. Kenanov A theoretical study using elementary flux modes Table 3. Elementary modes producing from adenosine. Elementary modes ADA AK PNPase RT 1. (3 PGI) (3 ALD) (3 TPI) (6 GAPDH) (6 PGM) (6 EN) (6 LACex) ()2 ApK) (3 HK) (3 PFK) (6 PGK) (6 PK) (6 LDH) (2 AK) 3 GLC +2 ADO ¼ 6 LACext ()6 PGI) (3 GAPDH) (3 PGM) (3 EN) (3 LACex) ApK (9 PGLase) (18 GSSGR) (3 R5PI) (6 Xu5PE) (3 TKI) (3 TKII) (3 TA) (3 HK) (3 PGK) (3 PK) (3 LDH) (18 GSHox) (9 G6PD) (9 GL6PDH) AK 3 GLC + ADO ¼ 9CO LACext + 3. (6 ALD) (6 TPI) (15 GAPDH) (15 PGM) (15 EN) (15 LACex) ( ApK) (9 PGLase) (18 GSSGR) (3 R5PI) (6 Xu5PE) (3 TKI) (3 TKII) (3 TA) (9 HK) (6 PFK) (15 PGK) (15 PK) (15 LDH) (18 GSHox) (9 G6PD) (9 GL6PDH) (5 AK) 9 GLC +5 ADO ¼ 9CO LACext ( 6 PGI) (3 GAPDH) (3 DPGM) (3 PGM) (3 EN) (3 LACex) ApK (6 PGLase) (12 GSSGR) (6 Xu5PE) (3 TKI) (3 TKII) (3 TA) (3PNPase) (3 PRM) (3 HXtrans) (3 DPGase) (3 PK) (3 LDH) (12 GSHox) (3 ADA) (6 G6PD) (6 GL6PDH) AK 4 ADO ¼ 3 HYPXext + 6 CO 2 + 3LACext + 5. ()6 PGI) (3 GAPDH) (3 PGM) (3 EN) (3 LACex) ()2 ApK) (6 PGLase) (12 GSSGR) (6 Xu5PE) (3 TKI) (3 TKII) (3 TA) (3 PNPase) (3 PRM) (3 HXtrans) (3 PGK) (3 PK) (3 LDH) (12 GSHox) (3 ADA) (6 G6PD) (6 GL6PDH) (2 AK) 5 ADO ¼ 3 HYPXext + 6 CO LACext ()6 PGI) (3 GAPDH) (3 PGM) (3 EN) (3 LACex) ApK (6 PGLase) (12 GSSGR) (6 Xu5PE) (3 TKI) (3 TKII) (3 TA) (3 PNPase) (3 PRM) (3 HXtrans) (3 PGK) (3 PK) (3 LDH) (3 AMPDA) (12 GSHox) (3 IMPase) (6 G6PD) (6 GL6PDH) (4 AK) 4 ADO ¼ 3 HYPXext + 6 CO LACext + 7. (2 ALD) (2 TPI) (5 GAPDH) (5 DPGM) (5 PGM) (5 EN) (5 LACex) ApK ()2 R5PI) (2 Xu5PE) TKI TKII TA (3 PNPase) (3 PRM) (3 HXtrans) (2 PFK) (5 DPGase) (5 PK) (5 LDH) (3 ADA) AK 4 ADO ¼ 3 HYPXext +5 LACext + 8. (6 ALD) (6 TPI) (15 GAPDH) (15 PGM) (15 EN) (15 LACex) ()8 ApK) ()6 R5PI) (6 Xu5PE) (3 TKI) (3 TKII) (3 TA) (9 PNPase) (9 PRM) (9 HXtrans) (6 PFK) (15 PGK) (15 PK) (15 LDH) (9 ADA) (8 AK) 17 ADO ¼ 9 HYPXext + 15 LACext (6 ALD) (6 TPI) (15 GAPDH) (15 PGM) (15 EN) (15 LACex) ()5 ApK) ()6 R5PI) (6 Xu5PE) (3 TKI) (3 TKII) (3 TA) (9 PNPase) (9 PRM) (9 HXtrans) (6 PFK) (15 PGK) (15 PK) (15 LDH) (9 AMPDA) (9 IMPase) (14 AK) 14 ADO ¼ 9 HYPXext + 15 LACext (2 ALD) (2 TPI) (5 GAPDH) (5 PGM) (5 EN) (5 LACex) ()2 ApK) (2 PGLase) (4 GSSGR) (2 Xu5PE) TKI TKII TA PNPase PRM HXtrans (2 HK) (2 PFK) (5 PGK) (5 PK) (5 LDH) (4 GSHox) ADA (2 G6PD) (2 GL6PDH) (2 AK) 2 GLC + 3 ADO ¼ HYPXext + 2 CO LACext (6 ALD) (6 TPI) (15 GAPDH) (15 DPGM) (15 PGM) (15 EN) (15 LACex) ApK (6 PGLase) (12 GSSGR) (6 Xu5PE) (3 TKI) (3 TKII) (3 TA) (3 PNPase) (3 PRM) (3 HXtrans) (6 HK) (6 PFK) (15 DPGase) (15 PK) (15 LDH) (12 GSHox) (3 ADA) (6 G6PD) (6 GL6PDH) AK 6 GLC + 4 ADO ¼ 3 HYPXext + 6 CO LACext (6 ALD) (6 TPI) (15 GAPDH) (15 PGM) (15 EN) (15 LACex) ( ApK) (6 PGLase) (12 GSSGR) (6 Xu5PE) (3 TKI) (3 TKII) (3 TA) (3 PNPase) (3 PRM) (3 HXtrans) (6 HK) (6 PFK) (15 PGK) (15 PK) (15 LDH) (3 AMPDA) (12 GSHox) (3 IMPase) (6 G6PD) (6 GL6PDH) (8 AK) 6 GLC + 8 ADO ¼ 3 HYPXext + 6 CO LACext in detail, we performed a simulation with the complete scheme shown in Fig. 1; that is, including at least one methyltransferase (considered irreversible in the direction of S-adenosylmethionine consumption) and SAHH. In that simulation, adenine and adenosine were considered internal, while S-adenosylmethionine was treated as external. This gave rise to 214 elementary modes (Supplementary Table S3). Twenty-three modes produce (Table 4). Some of them involve the modes starting from adenine obtained in the first simulation and include methyltransferase and SAHH2 in addition. Some others involve the modes starting from adenosine obtained in the second simulation and include methyltransferases and SAHH1 in addition. Interestingly, some modes involve both SAHH1 and SAHH2. FEBS Journal 272 (2005) ª 2005 FEBS 5283

7 A theoretical study using elementary flux modes S. Schuster and D. Kenanov Table 4. producing modes in the extended system including SAHH and methyltransferase. Elementary modes ADA AK PNPase RT Through SAHH1 but not SAHH2 1. (3 DPGase) (3 PK) (3 LDH) (4 MT) (12 GSHox) (3 ADA) (6 G6PD) (6 GL6PDH) AK ( 6 PGI) (3 GAPDH) (3 DPGM) (3 PGM) (3 EN) (3 LACex) -ApK (6 PGLase) (12 GSSGR) (6 Xu5PE) (3 TKI) (3 TKII) (3 TA) (3 PNPase) (3 PRM) (3 HXtrans) (4 SAHH1) 4 SAM + 4 H 2 O+4Acc¼3 HYPXext + 6 CO HCY LACext + 4 MetAcc 2. (3 PGK) (3 PK) (3 LDH) (5 MT) (12 GSHox) (3 ADA) (6 G6PD) (6 GL6PDH) (2 AK) ()6 PGI) (3 GAPDH) (3 PGM) (3 EN) (3 LACex) ()2 ApK) (6 PGLase) (12 GSSGR) (6 Xu5PE) (3 TKI) (3 TKII) (3 TA) (3 PNPase) (3 PRM) (3 HXtrans) (5 SAHH1) 5 SAM + 5 H 2 O+5Acc¼3HYPXext + 6 CO 2 +5 HCY LACext + 5 AccMet 3. (3 PGK) (3 PK) (3 LDH) (3 AMPDA) (4 MT) (12 GSHox) (3 IMPase) (6 G6PD) (6 GL6PDH) (4 AK) ()6 PGI) (3 GAPDH) (3 PGM) (3 EN) (3 LACex) ApK (6 PGLase) (12 GSSGR) (6 Xu5PE) (3 TKI) (3 TKII) (3 TA) (3 PNPase) (3 PRM) (3 HXtrans) (4 SAHH1) 4 SAM + 4 H 2 O+4Acc¼3HYPXext + 6 CO HCY LACext + 4 AccMet 4. (2 PFK) (5 DPGase) (5 PK) (5 LDH) (4 MT) (3 ADA) AK (2 ALD) (2 TPI) (5 GAPDH) (5 DPGM) (5 PGM) (5 EN) (5 LACex) ApK ()2 R5PI) (2 Xu5PE) TKI TKII TA (3 PNPase) (3 PRM) (3 HXtrans) (4 SAHH1) 4 SAM +4 H 2 O+4Acc¼ 3 HYPXext + 4 HCY LACext + 4 AccMet 5. (6 PFK) (15 PGK) (15 PK) (15 LDH) (17 MT) (9 ADA) (8 AK) (6 ALD) (6 TPI) (15 GAPDH) (15 PGM) (15 EN) (15 LACex) ()8 ApK) ()6 R5PI) (6 Xu5PE) (3 TKI) (3 TKII) (3 TA) (9 PNPase) (9 PRM) (9 HXtrans) (17 SAHH1) 17 SAM +17 H 2 O +17 Acc ¼ 9 HYPXext + 17 HCY LACext +17 AccMet 6. (6 PFK) (15 PGK) (15 PK) (15 LDH) (9 AMPDA) (14 MT) (9 IMPase) (14 AK) (6 ALD) (6 TPI) (15 GAPDH) (15 PGM) (15 EN) (15 LACex) ()5 ApK) ()6 R5PI) (6 Xu5PE) (3 TKI) (3 TKII) (3 TA) (9 PNPase) (9 PRM) (9 HXtrans) (14 SAHH1) 14 SAM +14 H 2 O + 14 Acc ¼ 9 HYPXext +14 HCY LACext + 14 AccMet 7. (3 HK) (3 PGK) (3 PK) (3 LDH) MT (18 GSHox) (9 G6PD) (9 GL6PDH) AK ()6 PGI) (3 GAPDH) (3 PGM) (3 EN) (3 LACex) ApK (9 PGLase) (18 GSSGR) (3 R5PI) (6 Xu5PE) (3 TKI) (3 TKII) (3 TA) SAHH1 SAM + H 2 O + Acc +3 GLC ¼ 9CO 2 + HCY + +3 LACext + AccMet 8. (6 HK) (6 PFK) (15 DPGase) (15 PK) (15 LDH) (4 MT) (12 GSHox) (3 ADA) (6 G6PD) (6 GL6PDH) AK (6 ALD) (6 TPI) (15 GAPDH) (15 DPGM) (15 PGM) (15 EN) (15 LACex) ApK (6 PGLase) (12 GSSGR) (6 Xu5PE) (3 TKI) (3 TKII) (3 TA) (3 PNPase) (3 PRM) (3 HXtrans) (4 SAHH1) 4 SAM + 4 H 2 O + 4 Acc + 6 GLC ¼ 3 HYPXext + 6 CO HCY LACext + 4 AccMet 9. (3 HK) (3 PFK) (6 PGK) (6 PK) (6 LDH) (2 MT) (2 AK) (3 PGI) (3 ALD) (3 TPI) (6 GAPDH) (6 PGM) (6 EN) (6 LACex) ()2 ApK) (2 SAHH1) 2 SAM +2 H 2 O + 2 Acc + 3 GLC ¼ 2 HCY LACext + 2 AccMet 10. (9 HK) (6 PFK) (15 PGK) (15 PK) (15 LDH) (5 MT) (18 GSHox) (9 G6PD) (9 GL6PDH) (5 AK) (6 ALD) (6 TPI) (15 GAPDH) (15 PGM) (15 EN) (15 LACex) ( 5 ApK) (9 PGLase) (18 GSSGR) (3 R5PI) (6 Xu5PE) (3 TKI) (3 TKII) (3 TA) (5 SAHH1) 5 SAM +5 H2O +5 Acc +9 GLC ¼ 9 CO2 +5 HCY LACext +5 AccMet 11. (2 HK) (2 PFK) (5 PGK) (5 PK) (5 LDH) (3 MT) (4 GSHox) ADA (2 G6PD) (2 GL6PDH) (2 AK) (2 ALD) (2 TPI) (5 GAPDH) (5 PGM) (5 EN) (5 LACex) ()2 ApK) (2 PGLase) (4 GSSGR) (2 Xu5PE) TKI TKII TA PNPase PRM HXtrans (3 SAHH1) 3 SAM +3 H 2 O + 3 Acc + 2 GLC ¼ HYPXext + 2 CO HCY LACext + 3 AccMet 12. (6 HK) (6 PFK) (15 PGK) (15 PK) (15 LDH) (3 AMPDA) (8 MT) (12 GSHox) (3 IMPase) (6 G6PD) (6 GL6PDH) (8 AK) (6 ALD) (6 TPI) (15 GAPDH) (15 PGM) (15 EN) (15 LACex) ()5 ApK) (6 PGLase) (12 GSSGR) (6 Xu5PE) (3 TKI) (3 TKII) (3 TA) (3 PNPase) (3 PRM) (3 HXtrans) (8 SAHH1) 8 SAM + 8 H 2 O + 8 Acc + 6 GLC ¼ 3 HYPXext + 6 CO HCY LACext + 8 AccMet Through SAHH1 & SAHH2 1. (4 DPGase) (4 PK) (4 LDH) (6 MT) RT (16 GSHox) PRPPsyn (5 ADA) (8 G6PD) (8 GL6PDH)()8 PGI) (4 GAPDH) (4 DPGM) (4 PGM) (4 EN) (4 LACex) ( 2 ApK) (8 PGLase) (16 GSSGR) (8 Xu5PE) (4 TKI) (4 TKII) (4 TA) (5 PNPase) (5 PRM) (5 HXtrans) SAHH2 (5 SAHH1) 6 SAM + 6 H 2 O+6Acc¼ 5 HYPXext + 8 CO 2 +6 HCY LACext + 6 AccMet + 3KRibose FEBS Journal 272 (2005) ª 2005 FEBS

8 S. Schuster and D. Kenanov A theoretical study using elementary flux modes Table 4. Continued. Elementary modes ADA AK PNPase RT 2. (2 PGK) (2 PK) (2 LDH) (4 MT) RT (8 GSHox) PRPPsyn (3 ADA) (4 G6PD) (4 GL6PDH) ( 4 PGI) (2 GAPDH) (2 PGM) (2 EN) (2 LACex) ( 2 ApK) (4 PGLase) (8 GSSGR) (4 Xu5PE) (2 TKI) (2 TKII) (2 TA) (3 PNPase) (3 PRM) (3 HXtrans) SAHH2 (3 SAHH1) 4 SAM + 4 H2O + 4 Acc ¼ 3 HYPXext + 4 CO2 +4 HCY LACext + 4 AccMet + 3KRibose 3. (8 PFK) (20 DPGase) (20 PK) (20 LDH) (18 MT) (3 RT) (3 PRPPsyn) (15 ADA) (8 ALD) (8 TPI) (20 GAPDH) (20 DPGM) (20 PGM) (20 EN) (20 LACex) ()6 ApK) ()8 R5PI) (8 Xu5PE) (4 TKI) (4 TKII) (4 TA) (15 PNPase) (15 PRM) (15 HXtrans) (3 SAHH2) (15 SAHH1) 18 SAM + 18 H 2 O + 18 Acc ¼ 15 HYPXext + 18 HCY LACext + 18 AccMet + 3 3KRibose 4. (2 PFK) (5 PGK) (5 PK) (5 LDH) (7 MT) (2 RT) (2 PRPPsyn) (5 ADA) (2 ALD) (2 TPI) (5 GAPDH) (5 PGM) (5 EN) (5 LACex) ()4 ApK)()2 R5PI) (2 Xu5PE) TKI TKII TA (5 PNPase) (5 PRM) (5 HXtrans) (2 SAHH2) (5 SAHH1) 7 SAM + 7 H 2 O+7Acc¼ 5 HYPXext + 7 HCY LACext + 7 AccMet + 2 3KRibose 5. (8 HK) (8 PFK) (20 DPGase) (20 PK) (20 LDH) (6 MT) RT (16 GSHox) PRPPsyn (5 ADA) (8 G6PD) (8 GL6PDH) (8 ALD) (8 TPI) (20 GAPDH) (20 DPGM) (20 PGM) (20 EN) (20 LACex) ( 2 ApK) (8 PGLase) (16 GSSGR) (8 Xu5PE) (4 TKI) (4 TKII) (4 TA) (5 PNPase) (5 PRM) (5 HXtrans) SAHH2 (5 SAHH1) 6 SAM + 6 H 2 O + 6 Acc + 8 GLC ¼ 5 HYPXext + 8 CO HCY LACext + 6 AccMet + 3KRibose 6. (2 HK) (2 PFK) (4 PGK) (4 PK) (4 LDH) (2 MT) RT PRPPsyn ADA (2 PGI) (2 ALD) (2 TPI) (4 GAPDH) (4 PGM) (4 EN) (4 LACex) ()2 ApK) PNPase PRM HXtrans SAHH2 SAHH1 2 SAM + 2 H 2 O + 2 Acc + 2 GLC ¼ HYPXext + 2 HCY LACext + 2 AccMet + 3KRibose 7. (4 HK) (4 PFK) (10 PGK) (10 PK) (10 LDH) (8 MT) (3 RT) (8 GSHox) (3 PRPPsyn) (5 ADA) (4 G6PD) (4 GL6PDH) (4 ALD) (4 TPI) (10 GAPDH) (10 PGM) (10 EN) (10 LACex) ()6 ApK) (4 PGLase) (8 GSSGR) (4 Xu5PE) (2 TKI) (2 TKII) (2 TA) (5 PNPase) (5 PRM) (5 HXtrans) (3 SAHH2) (5 SAHH1) 8 SAM + 8 H 2 O + 8 Acc + 4 GLC ¼ 5 HYPXext + 4 CO HCY LACext + 8 AccMet + 3 3KRibose Through SAHH2 only 1. (5 PK) (5 LDH) MT RT (32 GSHox) PRPPsyn (16 G6PD) (16 GL6PDH) ()10 PGI) (5 GAPDH) (5 PGM) (5 EN) (5 LACex) ()2 ApK) (16 PGLase) (32 GSSGR) (6 R5PI) (10 Xu5PE) (5 TKI) (5 TKII) (5 TA) SAHH2 SAM + H 2 O+Acc+6GLC¼16 CO 2 + HCY LACext + AccMet + 3KRibose 2. (10 HK) (8 PFK) (15 PGK) (15 PK) (15 LDH) (3 MT) (3 RT) (3 PRPPsyn) (10 PGI) (8 ALD) (8 TPI) (15 GAPDH) (15 PGM) (15 EN) (15 LACex) ()6 ApK) (2 R5PI) ()2 Xu5PE) TKI TKII TA (3 SAHH2) 3 SAM + 3 H 2 O + 3 Acc +10 GLC ¼ 3 HCY LACext + 3 AccMet + 3 3KRibose 3. (4 HK) (2 PFK) (5 PGK) (5 PK) (5 LDH) MT RT (8 GSHox) PRPPsyn (4 G6PD) (4 GL6PDH) (2 ALD) (2 TPI) (5 GAPDH) (5 PGM) (5 EN) (5 LACex) ()2 ApK) (4 PGLase) (8 GSSGR) (2 R5PI) (2 Xu5PE) TKI TKII TA SAHH2 SAM + H 2 O+Acc+4GLC¼4CO 2 + HCY LACext + AccMet + 3KRibose 4. (7 HK) (5 PFK) (10 PGK) (10 PK) (10 LDH) (2 MT) (2 RT) (4 GSHox) (2 PRPPsyn) (2 G6PD) (2 GL6PDH) (5 PGI) (5 ALD) (5 TPI) (10 GAPDH) (10 PGM) (10 EN) (10 LACex) ( 4 ApK) (2 PGLase) (4 GSSGR) (2 R5PI) (2 SAHH2) 2 SAM + 2 H 2 O + 2 Acc + 7 GLC ¼ 2CO HCY LACext + 2 AccMet + 2 3KRibose Note that operation of -producing pathways starting from S-adenosylmethionine permanently utilizes a methyl acceptor and produces the corresponding methylated form. In our simulation, we consider both substances to be external. A more detailed model may include a regeneration of the methyl acceptor from the methylated form or from other sources. Another possibility is to consider the following reaction mechanism. As SAHH1 is reversible, adenosine may react with homocysteine halfway and then (via the SAHH2 function) back to adenine, ribose and homocysteine. Thus, there is no net consumption of homocysteine in the process, and S-adenosylmethionine is not involved at all. Therefore, we performed a simulation with a model including the two functions of SAHH but excluding the methyltransferase (and, hence, S-adenosylmethionine). Adenosine was considered external. This produced 135 elementary modes (Supplementary FEBS Journal 272 (2005) ª 2005 FEBS 5285

9 A theoretical study using elementary flux modes S. Schuster and D. Kenanov Table 5. Elementary modes producing in the presence of SAHH (but not methyltransferase). There are 14 more modes not including SAHH but producing. Elementary modes ADA AK PNPase RT 1. (5 PGI) (5 ALD) (5 TPI) (10 GAPDH) (10 PGM) (10 EN) (10 LACex) ()4 ApK) (2 PGLase) (4 GSSGR) (2 R5PI) ()2 SAHH1) (7 HK) (5 PFK) (10 PGK) (10 PK) (10 LDH) (2 RT) (4 GSHox) (2 PRPPsyn) (2 G6PD) (2 GL6PDH) (2 SAHH2) 7 GLC + 2 ADO ¼ 2CO LACext + 2 3KRibose (10 PGI) (8 ALD) (8 TPI) (15 GAPDH) (15 PGM) (15 EN) (15 LACex) ()6 ApK) (2 R5PI) ( 2 Xu5PE) -TKI -TKII -TA ()3 SAHH1) (10 HK) (8 PFK) (15 PGK) (15 PK) (15 LDH) (3 RT) (3 PRPPsyn) (3 SAHH2) 10 GLC + 3 ADO ¼ 15 LACext + 3 3KRibose ()10 PGI) (5 GAPDH) (5 PGM) (5 EN) (5 LACex) ()2 ApK) (16 PGLase) (32 GSSGR) (6 R5PI) (10 Xu5PE) (5 TKI) (5 TKII) (5 TA) -SAHH1 (6 HK) (5 PGK) (5 PK) (5 LDH) RT (32 GSHox) PRPPsyn (16 G6PD) (16 GL6PDH) SAHH2 6 GLC + ADO ¼ 16 CO 2 +5 LACext + 3KRibose + 4. ()8 PGI) (4 GAPDH) (4 DPGM) (4 PGM) (4 EN) (4 LACex) ()2 ApK) (8 PGLase) (16 GSSGR) (8 Xu5PE) (4 TKI) (4 TKII) (4 TA) (5 PNPase) (5 PRM) (5 HXtrans) )SAHH1 (4 DPGase) (4 PK) (4 LDH) RT (16 GSHox) PRPPsyn (5 ADA) (8 G6PD) (8 GL6PDH) SAHH2 6 ADO ¼ 5 HYPXext + 8 CO LACext + 3KRibose + 5. ()4 PGI) (2 GAPDH) (2 PGM) (2 EN) (2 LACex) ()2 ApK) (4 PGLase) (8 GSSGR) (4 Xu5PE) (2 TKI) (2 TKII) (2 TA) (3 PNPase) (3 PRM) (3 HXtrans) SAHH1 (2 PGK) (2 PK) (2 LDH) RT (8 GSHox) PRPPsyn (3 ADA) (4 G6PD) (4 GL6PDH) SAHH2 4 ADO ¼ 3 HYPXext + 4 CO LACext + 3KRibose + 6. (8 ALD) (8 TPI) (20 GAPDH) (20 DPGM) (20 PGM) (20 EN) (20 LACex) ()6 ApK) ()8 R5PI) (8 Xu5PE) (4 TKI) (4 TKII) (4 TA) (15 PNPase) (15 PRM) (15 HXtrans) ()3 SAHH1) (8 PFK) (20 DPGase) (20 PK) (20 LDH) (3 RT) (3 PRPPsyn) (15 ADA) (3 SAHH2) 18 ADO ¼ 15 HYPXext + 20 LACext + 3 3KRibose (2 ALD) (2 TPI) (5 GAPDH) (5 PGM) (5 EN) (5 LACex) ()4 ApK)()2 R5PI) (2 Xu5PE) TKI TKII TA (5 PNPase) (5 PRM) (5 HXtrans) ()2 SAHH1) (2 PFK) (5 PGK) (5 PK) (5 LDH) (2 RT) (2 PRPPsyn) (5 ADA) (2 SAHH2) 7 ADO ¼ 5 HYPXext + 5 LACext + 2 3KRibose (2 PGI) (2 ALD) (2 TPI) (4 GAPDH) (4 PGM) (4 EN) (4 LACex) ()2 ApK) PNPase PRM HXtrans -SAHH1 (2 HK) (2 PFK) (4 PGK) (4 PK) (4 LDH) RT PRPPsyn ADA SAHH2 2 GLC + 2 ADO ¼ HYPXext + 4 LACext + 3KRibose + 9. (4 ALD) (4 TPI) (10 GAPDH) (10 PGM) (10 EN) (10 LACex) ( ApK) (4 PGLase) (8 GSSGR) (4 Xu5PE) (2 TKI) (2 TKII) (2 TA) (5 PNPase) (5 PRM) (5 HXtrans) ()3 SAHH1) (4 HK) (4 PFK) (10 PGK) (10 PK) (10 LDH) (3 RT) (8 GSHox) (3 PRPPsyn) (5 ADA) (4 G6PD) (4 GL6PDH) (3 SAHH2) 4 GLC + 8 ADO ¼ 5 HYPXext + 4 CO LACext + 3 3KRibose (8 ALD) (8 TPI) (20 GAPDH) (20 DPGM) (20 PGM) (20 EN) (20 LACex) ()2 ApK) (8 PGLase) (16 GSSGR) (8 Xu5PE) (4 TKI) (4 TKII) (4 TA) (5 PNPase) (5 PRM) (5 HXtrans) SAHH1 (8 HK) (8 PFK) (20 DPGase) (20 PK) (20 LDH) RT (16 GSHox) PRPPsyn (5 ADA) (8 G6PD) (8 GL6PDH) SAHH2 8 GLC + 6 ADO ¼ 5 HYPXext + 8 CO LACext + 3KRibose + Table S4) of which 10 generate from adenosine (Table 5). As expected, all of these use SAHH1 in the backward and SAHH2 in the forward direction. As can be seen in Table 5, both the glucose yield and adenosine yields are rather diverse. The highest values are 3 : 4 (in the modes really using glucose) and 1, respectively. However, they do not occur together, the elementary mode producing 3 mol of from 4 mol of glucose requires 8 mol of adenosine. As for the modes allowing an adenosine yield of 1, the highest glucose yield is 3 : 10. It is worth noting that there are 14 more modes not including SAHH but producing (Supplementary Table S4). Purine nucleoside phosphorylase, ADA, AK and RT deficiencies By checking which of the computed elementary modes remain after deleting a given enzyme, it can easily be analysed which salvage pathways can be operative in spite of severe enzyme deficiencies. If ADA is deficient, 5286 FEBS Journal 272 (2005) ª 2005 FEBS

10 S. Schuster and D. Kenanov A theoretical study using elementary flux modes all the four modes producing from adenine remain intact because they do not involve ADA (Table 2). Out of the 12 modes producing from adenosine, modes III.1-III.3, III.6, III.9, and III.12 remain intact. It is interesting that the other -producing modes (which drop out) involve ADA although it is an adenosine-degrading enzyme. Interestingly, the modes of adenine salvage (Table 2) are not affected at all by ADA, AK or purine nucleoside phosphorylase (PNPase) deficiencies. That is, these modes do not require these enzymes. However, they do require RT, which is in agreement with the experimental observation mentioned in the Introduction that patients deficient in RT are accumulating adenine [8 11]. The modes of adenosine salvage (Table 3) all require AK, so that they are not operative in the case of AK deficiency. This is clear because phosphorylation of adenosine is important in the buildup of from adenosine. Five out of 12 modes require ADA, AK and PNPase, and another three require AK and PNPase but not ADA. None of the 12 modes requires RT. The modes of buildup in the presence of SAHH1 (but not SAHH2) and methyltransferase (Table 4) all require AK but not R transferase. Six out of 12 modes require ADA, AK and PNPase and another three require AK and PNPase but not ADA. The modes in the presence of SAHH2 and MT (Table 4) do not require AK, while they do require RT, in agreement with experimental findings [9,10]. Interestingly, the pathways using SAHH2 but not SAHH1 are completely independent of the three enzymes ADA, AK and PNPase. Out of the 10 modes involving SAHH but not methyltransferase (Table 5), three modes do not require any of the enzymes ADA, AK and PNPase, the remaining seven require ADA and PNPase. AK is not required in any of the 10 modes. Interestingly, in these modes, it makes no difference whether ADA or PNPase are deleted, that is, a single deficiency in either enzyme has the same effect as the double deficiency. By contrast, in the modes of adenine salvage and adenosine salvage, deletion of PNPase is, on average, more critical than deletion of ADA. From Tables 2 5, it can easily be seen which elementary modes remain in the case of double or multiple deficiencies. For example, elementary mode 1 in Table 2 is still operating if ADA, AK and PNPase are deficient. In agreement with biochemical knowledge on human erythrocytes, HGPRT is not involved in any of the computed elementary modes corresponding to salvage pathways. Thus, hypoxanthine is not relevant for salvage in these cells. Conclusions We have analysed, by mathematical modelling, the buildup via salvage pathways in erythrocytes. Several authors used kinetic modelling to analyse erythrocyte metabolism [1,2,4]. We have used metabolic pathway analysis, which is a structural approach not requiring the knowledge of kinetic parameters. Pathway analysis has been applied to various enzyme deficiencies in the energy metabolism of erythrocytes [6] and to glutathione metabolism in a number of cells including erythrocytes [23]. Our results show once again that pathway analysis allows one to derive interesting conclusions about biochemical systems from a fairly limited amount of input information. The disadvantage is that dynamic effects cannot be analysed. When different disease states are to be studied, the metabolite levels at different time scales need to be considered. In that case, a dynamic model is preferable [2]. Earlier, we had calculated the elementary modes in a subnetwork involving the enzymes of nucleotide metabolism only [24]. One of the elementary modes obtained corresponds to part of an adenine salvage pathway. The system studied here is much more extended in that it involves glycolysis and the pentose phosphate pathway in addition. We have found four elementary modes producing starting from adenine. They involve parts of glycolysis and the pentose phosphate pathway in different proportions. As far as the pentose phosphate pathway is concerned, there is some interrelation to the modes found earlier for that system [14]. In particular, mode 1 (Table 2), which involves the oxidative pentose phosphate pathway and the enzyme R5PI, corresponds to the mode shown in Fig. 2D in Schuster et al. [14]. The modes II 2 4 correspond to the modes depicted in Fig. 2B,C,E, respectively [14]. However, R5PI is more active to provide the ribose necessary for buildup. Twelve pathways of buildup from adenosine have been found. However, only three of these convert adenosine completely into. The other nine transform some of it to hypoxanthine to obtain free energy. Thus, the latter cannot be considered as perfect salvage pathways. They also serve the purpose of purine transport by erythrocytes [25]. Our results predict that there is redundancy both in adenine salvage and in adenosine salvage in that parallel pathways producing from each of these substrates exist. While the metabolism of many cells is known to be redundant, this is surprising because erythrocyte metabolism in general has little redundancy and robustness. Earlier, we compared the structural FEBS Journal 272 (2005) ª 2005 FEBS 5287

11 A theoretical study using elementary flux modes S. Schuster and D. Kenanov robustness of Escherichia coli and erythrocytes and found that the latter is less robust [19]. In glycolysis, deletion of one enzyme (e.g. hexokinase) may suppress the entire pathway. Therefore, hexokinase or phosphofructokinase deficiencies have severe consequences [26]. Here, we have shown that the salvage pathways have a relatively high redundancy. This can be seen as a theoretical explanation of the clinical observation that deficiencies in the nucleotide metabolism of erythrocytes are usually less critical than deficiencies in enzymes of the energy metabolism of these cells and deficiencies in enzymes in the nucleotide metabolism of other cells such as lymphocytes. For example, no disease seems to be caused by PNPase deficiency in erythrocytes. This gives additional support for considering elementary mode analysis as an appropriate tool for metabolic pathways analysis [21]. It follows from our calculations that there is no salvage pathway starting from hypoxanthine. This is in agreement with experimental evidence for human erythrocytes because these cells lose, during development, the enzyme adenylosuccinate synthetase, which converts the first step leading from IMP to AMP [8]. From our theoretical analysis, a hitherto rarely discussed feature of the salvage pathways becomes transparent and understandable. This is the high number of molecules degraded in some part of each pathway while the total balance of production is positive. A molar investment ratio could be defined to express the number of moles of consumed divided by the difference between moles of produced and moles of consumed. The newly proposed molar investment ratio should not be confused with the usual concept of molar yield ; it only refers to one metabolite () and takes into account the consumption and formation of this, while the yield refers to two metabolites. The molar investment ratio quantifies how many are needed to trigger a pathway producing. In elementary mode 1 of adenine salvage (Table 2), this ratio is 18:(20 18) ¼ 9 : 1. Consider, for comparison, the glycolytic pathway. Two are invested at the upper end of the pathway while four are gained in the process, so that the difference is two. The molar investment ratio is one (2 : 2). In all salvage pathways found here, this ratio is much higher. Thus, a considerable effort in terms of enzyme activity is needed to build up by salvage pathways. It has sometimes been suggested that, if parallel pathways exist, living cells use the pathway with the highest yield [27] or obeying a minimum flux criterion [5]. It will be interesting to analyse, in the future, which of the salvage pathways are preferably used in vivo and whether they comply with these criteria. This, however, is beyond the scope of the present study, which is aimed at enumerating all potential pathways. Simmonds and coworkers [8 11] proposed a novel route of synthesis starting from S-adenosylmethionine or other nucleoside analogues. That route involves SAHH and is independent of AK but dependent on RT. We have examined whether this way of buildup is stoichiometrically and thermodynamically feasible. The result is positive. We found that this route is formed by a set of 11 slightly different pathways (Table 4). We found, second and additionally, third parts 12 pathways starting from S-adenosylmethionine involving the standard functionality of SAHH (here denoted as SAHH1) and another 10 pathways starting from adenosine (rather than S-adenosylmethionine) and involving SAHH1 in the backward direction and SAHH2 in the forward direction. This is a novel result because these pathways do depend on AK (whereas Simmonds and coworkers [8 11] only spoke about a pathway independent of AK). Interestingly, from Tables 4 and 5, it can be seen that the modes involving SAHH1 and or SAHH2 do not depend on R transferase if they involve AK and vice versa. On the basis of elementary flux modes analysis, it can be said that, even though not easily provable experimentally, the rarely mentioned route via SAHH is rather important. It gives additional opportunities to the cell for generating. Moreover, its analysis can help better understand some diseases affecting nucleotide metabolism and, hence, improve the treatment of patients. Experimental procedures The reaction scheme of human erythrocyte metabolism analysed here is shown in Fig. 1, which is based on schemes analysed earlier [1,3]. Reversible reactions are depicted by bidirectional arrows; all other reactions are assumed to be irreversible. The network essentially involves the enzymes from the glycolytic pathway, pentose phosphate pathway and purine metabolism (Table 1). We take into account that both adenine and adenosine can be taken up by the erythrocyte. In addition to items in the previous schemes [1,3], we include enzymes from the class of methyltransferases (EC x). An example is provided by protein-l-isoaspartate O-methyltransferase (EC ). This enzyme plays a role in the methylation of haemoglobin [28]. Methyltransferases transfer the methyl group from S-adenosylmethionine to various acceptors: 5288 FEBS Journal 272 (2005) ª 2005 FEBS

12 S. Schuster and D. Kenanov A theoretical study using elementary flux modes S-adenosylmethionine þ acceptor! S-adenosylhomocysteine þ methylated acceptor Besides, we include the enzyme SAHH because it is present in erythrocytes [29]. SAHH usually catalyses the reaction: S-adenosylhomocysteine! adenosine þ homocysteine This function is here referred to as SAHH1 and is, in accordance with the database ExPASy-ENZYME ( us.expasy.org/enzyme/) assumed to be reversible. Also, it was found that in the SAHH reaction, the unstable intermediate 3-ketoadenosine occurs, which can spontaneously disintegrate into adenine and 3 -ketoribose [11,13]. This alternative reaction: S-adenosylhomocysteine! adenine þ 3 0 -ketoribose þ homocysteine is here referred to as SAHH2 and is assumed to be irreversible because the disintegration occurs spontaneously. The complete list of enzymes is given in Table 1. Of course, the considered scheme does not cover the complete erythrocyte metabolism. The choice of reactions was motivated mainly by earlier models, textbook knowledge about salvage pathways and energy metabolism, as well as our aim to analyse the pathways using S-adenosylmethionine. Regarding sensitivity of the model results to addition of enzymes, it is important that elementary modes have the favourable property that the set of elementary modes in the extended system contains the elementary modes of the original system as a subset [24]. A drawback of the method might be that this structural analysis does not take into account genetic regulation. However, in mature erythrocytes, gene expression does not play any role as erythrocytes do not have a nucleus. Thus, all enzymes considered in our model are indeed expressed and cannot be downregulated by genetic means, so that this drawback does not apply to such cells. In metabolic pathway analysis, usually a distinction is made between internal and external metabolites. Internal metabolites are intermediates that have to fulfil a balance equation at steady state, that is, their production must equal their consumption. External metabolites are the sources and sinks of the network and are assumed to have buffered concentrations ([30], which also gives a detailed explanation of terms in metabolic pathway analysis). In all simulations throughout the paper, we consider glucose, lactate, CO 2 and, as well as hypoxanthine, sodium and potassium outside the cell to be external substances. Elementary flux modes are computed by the program metatool, which was developed by Pfeiffer et al. [15] and is continuously refined in our group ( biologie.uni-jena.de/bioinformatik). Alternative programs for the same task are available, for example, fluxanalyzer [31] and scrumpy (Poolman, ScrumPy/). Acknowledgements The authors wish to thank Dr Kutlu U lgen (Istanbul) for very helpful discussions on the manuscript and the Deutsche Forschungsgemeinschaft (SPP 1063) for financial support. References 1 Joshi A & Palsson BO (1989) Metabolic dynamics in the human red cell. Part I. A comprehensive kinetic model. J Theor Biol 141, Schuster R & Holzhu tter HG (1995) Use of mathematical models for predicting the metabolic effect of large-scale enzyme activity alterations. Application to enzyme deficiencies of red blood cells. Eur J Biochem 229, Schuster S, Fell DA, Pfeiffer T, Dandekar T & Bork P (1998) Elementary modes analysis illustrated with human red cell metabolism. In. Biothermokinetics in the Post Genomic Era (Larsson C, Påhlman I-L & Gustafsson L, eds), pp Chalmers, Go teborg. 4 Jamshidi N, Edwards JS, Fahland T, Church GM & Palsson BO (2001) Dynamic simulation of the human red blood cell metabolic network. Bioinformatics 17, Holzhu tter HG (2004) The principle of flux minimization and its application to estimate stationary fluxes in metabolic networks. Eur J Biochem 271, C akiy r T, Tacer CS & U lgen KO (2004) Metabolic pathway analysis of enzyme-deficient human red blood cells. Biosystems 78, Stryer L (1995) Biochemistry. Freeman, NewYork. 8 Simmonds HA, Fairbanks LD, Duley JA & Morris GS (1989) formation from deoxyadenosine in human erythrocytes: a hitherto unidentified route involving adenine and S-adenosylhomocysteine hydrolase. Biosci Report 9, Montero C, Smolenski RT, Duley JA & Simmonds HA (1990) S-Adenosylmethionine increases erythrocyte in vitro by a route independent of adenosine kinase. Biochem Pharmacol 40, Smolenski RT, Fabianovska-Majewska K, Montero C, Duley JA, Fairbanks LD, Marlewski M & Simmonds HA (1992) A nouvel route of synthesis. Biochem Pharmacol 43, Smolenski RT, Montero C, Duley JA & Simmonds HA (1991) Effects of adenosine analogues on concentrations in human erythrocytes: Further evidence for a route independent of adenosine kinase. Biochem Pharmacol 42, Chiang PK, Guranowski A & Segall JE (1981) Irreversible inhibition of S-adenosylhomocysteine hydrolase FEBS Journal 272 (2005) ª 2005 FEBS 5289